It is well-known that the 4-clique \(K_4\)  admits two embeddings, as a
planar tetrahedron and 1-planar with a pair of crossing edges. The
5-clique \(K_5\)  has five embeddings [1]}, as shown in
Fig. REF . Only the so-called T-embedding
in Fig. REF (a) is fan-crossing free and even
1-planar. The embedding in Fig. REF (e) has an edge which
is crossed by the edges of triangle. It is 1-gap-planar and
quasi-planar and not fan-crossing and not 2-planar. In fan-crossing
embeddings it can be transformed into
the Q-embedding of Fig. REF (c) [2]}.

